Not knowing the details of the judgement, a shut down seems a bit heavy handed and only more likely to bring scorn/attention to Apex (this despite the fact, I disagree with what these opposition groups are advocating).
On one hand I sympathize with Apex in that it seems fundamentally wrong that there are those who can attack you with impunity and anonymously online - particularly if they're lying about it. On the other, pursuing court action especially since it is unlikely that those running these sites have deep pockets seems like a PR disaster in the making (not to mention the fact that I think most readers take anonymous postings with a big grain of salt anyway - the legal suit for some will lend legitimacy to those false claims with many suspecting that 'the lady doth protest too much' and that their point may just be about revealing who those posters are to take retribution).